Twice-Universal Denoising

Erik Ordentlich,Krishnamurthy Viswanathan,Marcelo J Weinberger

doi:10.1109/tit.2012.2216503

Erik Ordentlich, Krishnamurthy Viswanathan + Show 1 more

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https://doi.org/10.1109/tit.2012.2216503

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Abstract

We propose a sequence of universal denoisers motivated by the goal of extending the notion of twice-universality from universal data compression theory to the sliding window denoising setting. Given a sequence length n and a denoiser, the k th-order regret of the latter is the maximum excess expected denoising loss relative to sliding window denoisers with window length 2 k +1, where, for a given clean sequence, the expectation is over all channel realizations and the maximum is over all clean sequences of length n . We define the twice-universality penalty of a denoiser as its excess k th-order regret when compared to a bound on the k th-order regret of the denoising algorithm DUDE with parameter k , and we are interested in denoisers with a negligible penalty for all k simultaneously. We consider a class of denoisers that apply one of a number of constituent denoisers based on minimizing an estimated denoising loss and establish a formal relationship between the error in the estimated denoising loss and the twice-universality penalty of the resulting denoiser. Given a sequence of window parameters kn , increasing in n sufficiently fast, we use this approach to construct and analyze a specific sequence of denoisers that achieves a much smaller twice-universality penalty for k <; kn than the sequence of DUDE denoisers with parameter kn .

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